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A 1,400-kg automobile moving with a speed of 24 m/s relative to the road collides with a 700-kg automobile initially at rest. If the two stick together, what is the velocity in m/s of the two cars after the collision according to an observer in a truck moving 11 m/s in the same direction as the moving cars?

6.0

19

5.0

21

1.0

A 1,000-kg automobile moving with a speed of 27 m/s collides with a 500-kg car initially at rest. If the two stick together, what is the velocity (in m/s) of the two cars after the collision relative to an automobile moving in the same direction at 15 m/s?

4.0

5.0

3.0

21

23

1.

2.

3.

4.

5.

A boat has an initial velocity of 5 m/s in the {image} -direction on a stream which is moving in the {image} -direction at 1 m/s. The boat is accelerating in its direction of motion at {image} What is the acceleration of the boat (in {image} ) relative to the water?

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A spaceship moves at a speed of {image} away from the Earth. It shoots a star wars torpedo toward the Earth at a speed of {image} relative to the ship. What is the velocity of the torpedo relative to the Earth? (The direction in which the spaceship moves is the positive direction.)

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A satellite moves east, taken as the positive {image} -axis direction, at a speed of {image} and a spaceship moves toward it (to the west) at a speed of {image} as measured by an observer on the Earth. Find the speed of the satellite measured by an observer in the spaceship.

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A fancy sports car passes Big Ben at a speed of {image} What time interval will the driver measure for a one-second interval on the large clock?

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A fancy sports car moves past an observer on a corner at a speed of {image} When the observer indicates a one-second interval has passed, what time interval will be shown on the driver's watch?

{image}

{image}

{image}

{image}

{image}

Two fireworks explode at the same position on the 4th of July. A stationary observer notices that the time interval between the two events was 3.00 seconds. A second observer flies past the fireworks at a speed of {image} What value does she obtain when she measures the time interval between the two explosions?

1.9 s

3.75 s

3.0 s

2.4 s

4.29 s

The half-life of a muon is {image} as measured in a stationary reference frame. What is the half life of the muon (in {image} ) when it is moving with a speed of {image}

15.8

1.22

2.24

2.63

1.68

1.

2.

3.

4.

5.

The half-life of a muon is {image} How fast is it moving relative to an observer who says its half-life is {image}

{image}

{image}

{image}

{image}

{image}

A spaceship moving past the Earth with a speed of {image} signals to the Earth with pulsed laser photons emitted at 14-second intervals according to the spaceship's clock. According to observers on Earth who see the flashes, what is the time interval they measure?

4.0 s

40.4 s

50.1 s

32.1 s

6.1 s

A 35-year-old woman takes a trip on a rocket, leaving her 20-year-old brother behind. She travels at a speed of {image} and is gone 10 years, according to the younger brother. When she returns, how many years older/younger is she than her brother?

11 years older

16 years older

12 years older

23 years older

11 years younger

A jet plane travels around the world at 2,200 mi/hr (983 m/s). Two accurate atomic clocks measure the times of flight, one on board the plane and the second on Earth. If it takes 11 hours to complete the journey, what will the time difference (in {image} ) be?

0.23

0.21

0.52

1.7

0.15

A meterstick is shot from a meterstick projector at a speed of {image} How long will it be relative to an observer's frame of reference?

1.0 m

0.80 m

1.2 m

0.84 m

0.90 m

A starship navigator measures the distance between the Earth and the sun. If the ship is moving at a speed of {image} instead of obtaining 93 million miles, what distance (in millions of miles) does the navigator measure?

122

78

68

85

71

An astronaut traveling with a speed {image} holds a meterstick in his hand. If he measures its length, what value will he obtain?

1.3 m

0.89 m

1 m

0.76 m

0.73 m

1.

2.

3.

4.

5.

An electron {image} has a speed of {image} Determine the difference between its relativistic kinetic energy and the kinetic energy calculated without considering relativity.

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

An electron has a kinetic energy that is four times its rest energy. Determine its speed.

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

An electron {image} has a speed of {image} What is the difference between its relativistic momentum and its non-relativistic momentum (in kg m/s)?

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A proton's rest mass is {image} Calculate its total energy when it is accelerated to a speed of {image}

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A proton's rest mass is {image} Calculate its total kinetic energy when it is accelerated to a speed of {image}

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

Energy is released during a nuclear reaction due to a conversion between mass and energy. Mass is not conserved. The initial and final amounts are different. If a total of 6 g of mass is "missing", how much energy has been released?

{image}

{image}

{image}

{image}

{image}

Assume a g of a substance marketed as "Pure Energy" is annihilated by g of a second substance "Anti-Pure Energy." How long would the energy released power a city which uses {image} watts of power?

50,000 hrs

50 hrs

40 hrs

35 hrs

55 hrs

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2.

3.

4.

5.

A proton has a total energy of {image} How fast is it moving? {image}

{image}

{image}

{image}

{image}

{image}

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2.

3.

4.

5.

A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure that distance to be {image} ) On Earth, the spaceship is observed to be traveling at a speed of {image} for which {image} As measured on Earth it takes the spaceship 833 seconds to travel from the sun to Earth. If a scientist in the spaceship measures the Earth-sun distance and the time it takes her to travel that distance, what results will she find?

{image}

{image}

{image}

{image}

{image}

2.

1.

3.

4.

5.

Fireworks go off at the same time according to Earth clocks in two cities, Alum and Boron, that are 400 km apart. The people in a spaceship that is flying in a straight line from Alum to Boron at {image} also observe the fireworks. Do they see the fireworks in the two cities simultaneously? If the people in the spaceship say the fireworks were not simultaneous in Alum and Boron, how long before or after the fireworks flashed at Alum did the fireworks flash at Boron according to their calculations? (The spaceship is directly over Alum when the fireworks flash.)

Yes; {image}

After; {image}

After; {image}

Before; {image}

Before; {image}

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2.

3.

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5.

The first intergalactic spaceship is headed toward the Magellanic Clouds at a speed of {image} The spaceship is 4,000 m long. Clocks at the front and the rear of the spaceship both read 7:00 P.M. Can it be 7:00 P.M. simultaneously at the front and the back of the spaceship?

Yes, because {image} in (a) is zero for different points of the same spaceship.

No, because {image} where {image} is the length of the spaceship.

No, because one clock has to move after being synchronized with the other.

The question cannot be answered unless we know the object relative to which the spaceship's velocity is {image}

Yes, because two clocks at rest relative to each other can be synchronized by means of light signals when the distance between them is known.

1.

2.

3.

4.

5.

As a spaceship heads directly to Earth at a velocity of {image} it sends a radio signal to Earth. When those radio waves arrive on Earth, what is their velocity relative to Earth?

{image} where {image} is the velocity of the Earth

{image}

{image}

{image}

{image} where {image} is the velocity of the Earth

1.

2.

3.

4.

5.

The speed of FM waves will be observed to be {image} when the antenna emitting the waves is _____.

at rest relative to the receiving antenna

moving to the left of the detecting antenna at {image}

moving to the right of the detecting antenna at {image}

moving as described in a, b or c above.

moving at {image}

Captain Jirk reports to headquarters that he left the planet Senesca {image} seconds earlier. Headquarters sends back the message: "Was that spaceship proper time?" It will be spaceship proper time if it was ______.

measured by a clock on Senesca at departure and by a clock on the spaceship when reporting

measured by a clock on the spaceship when departing and by a clock on Senesca when reporting

measured by one clock fixed at one spot on Senesca

measured by one clock fixed at one spot on the spaceship

calculated by dividing the distance from Senesca according to Senesca by the speed of the spaceship

1.

2.

3.

4.

5.

In a classroom on the first spaceship to an extrasolar planet - there are children because the trip will take 200 years - a teacher is showing charge {image} uniformly distributed along a conducting rod of length {image} to produce linear charge density {image} As observed on Pluto when the spaceship passes it at {image} what is the linear charge density {image}

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

The quantity which does not change in magnitude from that observed in system {image} when observed in system {image} moving away from system {image} at speed {image} is

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

Hanna, at rest in her spaceship which is moving past Earth at {image} observes a neutron at rest relative to her spaceship decay into a proton, an electron and a neutrino. She notes that the total momentum, {image} of the decay products is zero after the decay. According to an observer on Earth, what is the magnitude of the total momentum {image} of the decay products?

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A spaceship leaves Earth and maintains a constant force by means of a nuclear engine. As the speed of the spaceship increases, an observer on Earth finds that relative to her the magnitude of the spaceship's acceleration is _____.

0

decreasing

proportional to the kinetic energy of the spaceship

increasing

constant

Which observer in the figure below sees the ball's correct path? {image}

The observer in the truck.

The observer on the ground.

Both observers.

1.

2.

3.

4.

5.

A baseball pitcher with a 90-mi/h fast ball throws a ball while standing on a railroad flatcar moving at 110 mi/h. The ball is thrown in the same direction as that of the velocity of the train. Applying the Galilean velocity transformation equation, the speed of the ball relative to the Earth is _____.

90 mi/h

110 mi/h

20 mi/h

200 mi/h

impossible to determine

1.

2.

3.

4.

Suppose the observer {image} on the train in the figure below aims her flashlight at the far wall of the boxcar and turns it on and off, sending a pulse of light toward the far wall. Both {image} and {image} measure the time interval between when the pulse leaves the flashlight and it hits the far wall. {image} Which observer measures the proper time interval between these two events?

{image}

{image}

Both observers.

Neither observer.

A crew watches a movie that is two hours long in a spacecraft that is moving at high speed through space. An Earthbound observer, who is watching the movie through a powerful telescope, will measure the duration of the movie to be _____.

longer than two hours

shorter than two hours

equal to two hours

Suppose astronauts are paid according to the amount of time they spend traveling in space. After a long voyage traveling at a speed approaching {image} a crew would rather be paid according to _____.

an Earth-based clock

their spacecraft's clock

either clock

You are packing for a trip to another star. During the journey, you will be traveling at {image} You are trying to decide whether you should buy smaller sizes of your clothing, because you will be thinner on your trip, due to length contraction. Also, you are considering saving money by reserving a smaller cabin to sleep in, because you will be shorter when you lie down. You should _____.

buy smaller sizes of clothing

reserve a smaller cabin

do neither of these

do both of these

You are observing a spacecraft moving away from you. You measure it to be shorter than when it was at rest on the ground next to you. You also see a clock through the spacecraft window, and you observe that the passage of time on the clock is measured to be slower than that of the watch on your wrist. Compared to when the spacecraft was on the ground, what do you measure if the spacecraft turns around and comes toward you at the same speed?

The spacecraft is measured to be longer and the clock runs faster.

The spacecraft is measured to be longer and the clock runs slower.

The spacecraft is measured to be shorter and the clock runs faster.

The spacecraft is measured to be shorter and the clock runs slower.

1.

2.

3.

You are driving on a freeway at a relativistic speed. Straight ahead of you, a technician standing on the ground turns on a searchlight and a beam of light moves exactly vertically upward, as seen by the technician. As you observe the beam of light, you measure the magnitude of the vertical component of its velocity as _____.

equal to {image}

greater than {image}

less than {image}

1.

2.

3.

You are driving on a freeway at a relativistic speed. Straight ahead of you, a technician standing on the ground aims the searchlight directly at you instead of upward. As you observe the beam of light you measure the magnitude of the horizontal component of its velocity as _____.

equal to {image}

greater than {image}

less than {image}

1.

2.

3.

4.

5.

6.

A physics professor on the Earth gives an exam to her students, who are in a spacecraft traveling at speed {image} relative to the Earth. The moment the craft passes the professor, she signals the start of the exam. She wishes her students to have a time interval {image} (spacecraft time) to complete the exam. What time interval (Earth time) should she wait before sending a light signal telling them to stop. (Suggestion: Remember that it takes some time for the second light signal to travel from the professor to the students.)

{image}

{image}

{image}

{image}

{image}

{image}

1.

2.

3.

4.

5.

A particle of mass {image} moving along the x axis with a velocity component {image} collides head-on and sticks to a particle of mass {image} moving along the x axis with the velocity component {image} . What is the mass {image} of the resulting particle?